The Little Higgs mechanism whose most minimal implementation, the
Littlest Higgs model [1]}, gives a solution to the
hierarchy problem: the Higgs is light because it is a
pseudo-Nambu-Golstone boson of some new global symmetry spontaneously
broken at scale \(f \sim \)  TeV. In order to evade severe constraints
from new strongly interacting sectors at the TeV scale, a collective
symmetry breaking mechanism introduces a quadratically cut-off
sensitive Higgs mass term only at the two-loop level and pushes an
underlying strong sector to the tens of TeV scale.
Despite this, electroweak precision observables (EWPO,
cf. e.g. [2]} still give tight constraints on Little
Higgs models, particularly from the oblique corrections to the vacuum
energies of the weak gauge bosons, such that the symmetry breaking
scale \(f\)  is limited to be larger than at least 3 TeV at 95 %
confidence level. In order to allow for much lower scales, a discrete
symmetry – TeV or T parity [3]} – has been
introduced. This symmetry relaxes the bound on \(f\)  by an order of
magnitude, and forces new particles to be pair-produced, and then
undergo cascade decays. The lightest T-odd particle (LTP), the heavy
photon partner \(A_H\) , is potentially stable. We investigate the
corresponding model, the Littlest Higgs model with T-parity (LHT) and
study the limits from the 8 and 13 TeV runs of the LHC from
direct searches of the new heavy vector bosons, heavy quark and lepton
partners predicted in this model. This study is based
on [4]} as well as on earlier work published
in [5]}, [6]}. Both due to tight constraints from
searches for Dark Matter as well as the possibility for \(T\) -breaking
UV completions, we also consider T-parity breaking.
